Towards maximal cell density predictions for polymeric foams

Abstract

Self-consistent field theory is used to make direct predictions for the maximum possible cell densities for model polymer foam systems without recourse to clas sical nucleation theory or activation barrier kinetic arguments. Maximum pos sible cell density predictions are also made subject to constraining the systems to have maximal possible internal interface and to have well formed bubbles (no deviation from bulk conditions on the interior of the bubble). This last condi tion is found to be the most restrictive on possible cell densities. Comparison is made with classical nucleation theory and it is found that the surface tension is not an important independent consideration for predicting conditions consistent with high cell density polymeric foams or achieving the smallest possible bub ble sizes. Instead, the volume free energy density, often labelled as a pressure difference, is the dominant factor for both cell densities and cell sizes.

Maximal cell density predictions for compressible polymer foams

“…The hole-based SCFT that we use in this work was first introduced by Hong and Noolandi [8]. As there are many very good reviews of SCFT, such as references [9] and [10], we will not present the details of SCFT here but rather refer the reader to our previous works for incompressible [2,3] and compressible [6,11] polymer foams. The SCFT model for a compressible polymer solvent system can however be summarized by the free energy functional…”

“…The formalism is used in a way that parallels reference [2]. We choose closeand φ 0 packed polymer and solvent volume fractions for the incompressible case, φ 0 p , and change the size of the calculational volume V to find the maximum s cell density.…”

“…One can choose to define the cell density as the number of cells per unit volume or the number of cells per unit volume of polymer [13]. We chose the latter in reference [2] and we follow this convention again in this work. Therefore the cell density is defined as the inverse of the product of the calculational box volume times the overall polymer volume fraction.…”

“…Recently, we introduced a method of predicting the maximum cell density of foams based on self-consistent field theory (SCFT) [2]. The method didn't predict an absolute cell density, but rather provided an upper bound that, from a thermodynamic perspective, real foams would be unlikely to exceed.…”

“…Nonetheless, one can use SCFT for polymer foaming as has been argued in references [3] and [4]. Our method was not quan titative however but rather provided only qualitative guidance such as finding that foaming should take place at as low a practical temperature as possible, that the maximum amount of blowing agent that doesn't cause spinodal de composition should be used, and that polymer surface tension is not always an important factor in predicting cell densities [2]. The root of the qualitative nature of our predictions was that we used, for simplicity, an incompressible model of polymer foaming.…”